The perimeter of equilateral $\Delta ABC$ is $24$. Find the length of its altitude. (in $\sqrt{3}$)

$\Delta PQR \sim \Delta DEF$ for the correspondence $PQR \leftrightarrow DEF$. If $3 PQ = 2 DE$,$EF = 6$,and $PR = 8$,find $QR$ and $DF$.

The length of a ladder is $6 \,m$ and it leans on a wall to reach the height of $3.6 \,m$. Find the distance in $m$ between the lower end of the ladder and the base of the wall.

In $\Delta XYZ$,$m \angle Y = 90^{\circ}$ and $XY : XZ = 15 : 17$. If $YZ = 4$,find the perimeter of $\Delta XYZ$.

The perimeter of an equilateral triangle is $18$. Then,the length of its altitude is $\ldots \ldots \ldots$

In $\square ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{M\}$. If $\frac{MB}{MD} = \frac{5}{3}$ and $CD = 12$,find $AB$.